* Liberals come in third in all four by-elections

* Conservatives pick up support in Quebec

* Liberal support started falling in September (Adds separatist, government comment, paragraphs 7-8, 13-14)

By Randall Palmer

OTTAWA, Nov 10 (Reuters) - Hurt by a poor showing in special elections on Monday, Canada's opposition Liberal Party acknowledged on Tuesday it has a steep hill to climb to regain popular support.

The Liberals, the biggest opposition party and the most successful political party in Canadian history, came in in third place in all four of Monday's elections, held to fill vacant seats in the federal Parliament.

The Liberals decided in September to try to bring down the minority Conservative government in Parliament and force a general election, but their dismal showing in Monday's by-elections, and an unexpected pickup in support for the Conservatives in the French-speaking province of Quebec, have prompted some soul-searching.

"The by-election results last night show that we have a lot of work ahead of us," said Liberal leader Michael Ignatieff, a former Harvard don who shook up his inner circle this month in a bid to rebuild momentum.

"Our job in the months ahead is to earn the confidence and support of Canadians."